Branching fraction of ${\tau }^{\mathbf{-}}\to {\pi }^{\mathbf{-}}{K}_s^0{K}_s^0\mathbf{(}{\pi }^0\mathbf{)}{\nu }_{\tau }$ decays

We present a study of ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0({\pi }^0){\nu }_{\tau }$ and ${\tau }^{-}\to K^{-}{K}_S^0{K}_S^0({\pi }^0){\nu }_{\tau }$ decays using a data set of 430 million $\tau$ lepton pairs, corresponding to an integrated luminosity of $468{\mathrm{fb}}^{-1}$, collected with the BABAR detector at the PEP-II asymmetric energy $e^{+}{e}^{-}$ storage rings. We measure branching fractions of $(2.31\pm 0.04\pm 0.08)\times {10}^{-4}$ and $(1.60\pm 0.20\pm 0.22)\times {10}^{-5}$ for the ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ and ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\pi }^0{\nu }_{\tau }$ decays, respectively. We find no evidence for ${\tau }^{-}\to K^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ and ${\tau }^{-}\to K^{-}{K}_S^0{K}_S^0{\pi }^0{\nu }_{\tau }$ decays and place upper limits on the branching fractions of $6.3\times {10}^{-7}$ and $4.0\times {10}^{-7}$ at the 90% confidence level.

Figure 1

The invariant mass of the two $K_S^0\to {\pi }^{+}{\pi }^{-}$ candidates in the ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ (top) and ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\pi }^0{\nu }_{\tau }$ (bottom) samples after all selection criteria have been applied. The points are data and the histograms are the prediction of the Monte Carlo simulation. For both plots, the white histogram represents ${\tau }^{-}\to K^{*-}{K}^0{\nu }_{\tau }$ decays, and the blue (medium shaded) and beige (light shaded) histogram shows the ${\tau }^{-}\to K^{*-}{K}^0{\pi }^0{\nu }_{\tau }$ and ${\tau }^{-}\to K^{*0}{K}^0{\pi }^{-}{\nu }_{\tau }$ ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\pi }^0{\nu }_{\tau }$) decays, respectively. The red (dark shaded) histogram is the $q\overline{q}$ background.

Figure 2

The Dalitz plot of the (${\pi }^{-}{K}_S^0$) system, and the (${\pi }^{-}{K}_S^0{K}_S^0$), (${\pi }^{-}{K}_S^0$) and ($K_S^0{K}_S^0$) invariant mass distributions for events that pass the ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ selection criteria. The invariant mass requirement is not required for the plot of the (${\pi }^{-}{K}_S^0{K}_S^0$) invariant mass. There are two entries per event in the Dalitz plot and in the (${\pi }^{-}{K}_S^0$) mass plot. The points are data and the histograms are the prediction of the Monte Carlo simulation. The signal decays are represented by the white histogram (${\tau }^{-}\to K^{*-}{K}^0{\nu }_{\tau }$). The beige (light shaded) histogram shows the ${\tau }^{-}\to K^{*-}{K}^0{\pi }^0{\nu }_{\tau }$ and ${\tau }^{-}\to K^{*0}{K}^0{\pi }^{-}{\nu }_{\tau }$ (${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\pi }^0{\nu }_{\tau }$) decays. The red (dark shaded) histogram is the $q\overline{q}$ background. The mass plots use ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ events that have been weighted based on the Dalitz plot distributions in the top left plot.

Figure 3

The (${\pi }^{-}{K}_S^0{K}_S^0$), (${\pi }^{-}{K}_S^0{K}_S^0{\pi }^0$), (${\pi }^{-}{K}_S^0$), and (${\pi }^0{K}_S^0$) invariant mass distributions that pass the ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\pi }^0{\nu }_{\tau }$ selection criteria [except for the plot of the (${\pi }^{-}{K}_S^0{K}_S^0$) invariant mass where the selection requirement on the mass is not included]. There are two entries per event in the (${\pi }^{-}{K}_S^0$) and (${\pi }^0{K}_S^0$) mass plots. The points are data and the histograms are the predictions of the Monte Carlo simulation. The two signal channels are shown in the white (${\tau }^{-}\to K^{*-}{K}^0{\pi }^0{\nu }_{\tau }$) and beige (light shaded) (${\tau }^{-}\to K^{*0}{K}^0{\pi }^{-}{\nu }_{\tau }$) histograms. The dark blue (medium shaded) histogram is ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ (${\tau }^{-}\to K^{*-}{K}^0{\nu }_{\tau }$) decays. The red (dark shaded) histogram is the $q\overline{q}$ background. The mass plots use ${\tau }^{-}\to {\pi }^{-}{K}_S^0{K}_S^0{\nu }_{\tau }$ events that have been weighted based on the Dalitz plot distributions shown in Fig. 2.